A method is proposed which simplifies estimation of all parameters in the functional measurement error model with no error in the equation under the assumption that the error covariance for the explanatory variables is known and the variance of the dependent variable is unknown. The proposed method is shown to produce the same estimates given for the both the structural model and the functional model with error in the equation in Schneeweiss (1976) and Fuller (1987). Simulation results indicate that for large sample sizes and even for moderate sample sizes, the maximum likelihood regression estimates one gets from assuming a structural measurement error model perform quite well in estimating the regression parameters in the functional measurement error model. © 1994, Taylor & Francis Group, LLC. All rights reserved.